A Berry-Esseen Type Bound of Wavelet Estimator Under Linear Process Errors Based on a Strong Mixing Sequence

Consider the nonparametric regression model Y-ni = g(t(ni)) + epsilon(ni), 1 <= i <= n ,where {t(ni)} are known design points, and the errors {epsilon(ni)} have a linear representation epsilon(ni) = Sigma(infinity)(j=-infinity) a(j)e(i-j) with Sigma(infinity)(i=-infinity) vertical bar a(i)vertical bar < infinity and {e(t), -infinity < t < infinity} are strong mixing random variables. g(center dot) is an unknown function defined on closed interval [0,1], which is estimated by a linear wavelet estimator <(g(n))over cap>(t). The main result of this article is that of providing, under certain regularity conditions, a Berry-Esseen boundary for the linear wavelet estimator (g(n)) over cap (t), and the Berry-Esseen bound can attain O(n(-1/6)).